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A stability theorem for Berge Hamiltonian cycles under a minimum degree condition
Yichen Wang, Dániel Gerbner, Xiamiao Zhao
In this paper, we study extremal and stability problems for Berge Hamiltonian cycles in -uniform hypergraphs under a minimum degree condition. Let $ g_r(n,t)=\binom{n-t}{r}+t\bi…
On the Turán number of blow-ups of
Xiamiao Zhao, Xin Cheng, Dániel Gerbner +4
Let denote the -uniform hypergraph on the vertex set with hyperedges . Recently, Balogh, Clemen and Lu…
On the largest chromatic number of -free hypergraphs
Yichen Wang, Mengyu Duan, Dániel Gerbner +1
Given a hypergraph , what is the largest chromatic number that an -free hypergraph can have? In the case of graphs, this question is easy to answer: the chromatic number is u…
On the connected Turán number of Berge paths and Berge cycles
Xiamiao Zhao, Dániel Gerbner, Junpeng Zhou
Given a graph , a Berge copy of (Berge- for short) is a hypergraph obtained by enlarging the edges arbitrarily. Győri, Salia and Zamora determined the maximum number of h…
Generalized Turán problems for Berge hypergraphs
Xiamiao Zhao, Xin Cheng, Dániel Gerbner
Let be a hypergraph and be a graph. If there exists a bijection between the hyperedges of and the edges of such that each hyperedge contains its…
A note on a very abstract chromatic number and extremal problems
Dániel Gerbner
The abstract chromatic number was introduced by Razborov and Coregliano in 2020 in using the language of model theory, and was used to extend the Erd\H os-Stone-Simonovits theorem…
A note on hyperseparating set systems
Dániel Gerbner
We say that a set system is -completely hyperseparating if for any vertex , there are at most sets in with intersection . We determine…
The Turán number of Berge paths
Xin Cheng, Dániel Gerbner, Hilal Hama Karim +2
A Berge path of length in an -uniform hypergraph is a collection of hyperedges and vertices such that for…